Question: The grades on a language midterm at Loyola are normally distributed with $\mu = 81$ and $\sigma = 4.5$. Christopher earned a $92$ on the exam. Find the z-score for Christopher's exam grade. Round to two decimal places.
Solution: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Christopher's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{92 - {81}}{{4.5}}} $ ${ z \approx 2.44}$ The z-score is $2.44$. In other words, Christopher's score was $2.44$ standard deviations above the mean.